Zara had some brown and pink balls. If she gives away 34 brown balls, the number of brown balls will be 10% of the total number of balls left. If she gives away 18 pink balls, the number of brown balls will be 25% of the total number of balls left.
- How many balls does Zara have altogether?
- What fraction of Zara's balls is pink?
| |
Scenario 1 |
Scenario 2 |
| |
Brown |
Pink |
Brown |
Pink |
| Before |
1 u + 34 |
9 u |
1 p |
3 p + 18 |
| Change |
- 34 |
No change |
No change |
- 18 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 34 = 1 p --- (1)
9 u = 3 p + 18
9 u - 18 = 3 p --- (2)
Make p the same.
(1)
x33 u + 102 = 3 p --- (3)
(2) = (3)
9 u - 18 = 3 u + 102
9 u - 3 u = 102 + 18
6 u = 120
1 u = 120 ÷ 6 = 20
Number of balls that Zara had at first
= 1 u + 34 + 9 u
= 10 u + 34
= 10 x 20 + 34
= 200 + 34
= 234
(b)
Number of pink balls
= 9 u
= 9 x 20
= 180
Fraction of Zara's balls that is pink
=
180234=
1013 Answer(s): (a) 234; (b)
1013 
